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Abstract

The propagation of a self-trapped laser beam in a planar waveguide that exhibits a Kerr nonlinearity and a normal chromatic dispersion is considered. We demonstrate experimentally for the first time to our knowledge that such a beam undergoes an undulation responsible for ultrafast transverse oscillations of its axis. This phenomenon, called “snake instability”, was predicted theoretically in 1973 by Zakharov and Rubenchik on the basis of a study of the soliton solutions of the hyperbolic nonlinear Schrödinger equation. The signature of this instability is observed in the spatially resolved temporal spectrum.

Figures (6)

Snake instability of laser beams. The interplay between normal dispersion, diffraction and Kerr nonlinearity leads to transverse undulations of self-trapped beams. The schematic on the right hand side explains that the periodic lateral beam shift results from the amplification of an antisymmetric unstable mode.

Laser beam profile at the output of the guiding structure. In the linear propagation regime, the beam broadens due to diffraction (top). At high power, the optical Kerr non-linearity balances the diffraction and a spatial soliton is formed (bottom).

Input and output spectra of the laser beam. Nonlinear effects within the laser source are responsible for the presence of small sidebands in the spectrum. When a soliton is formed, these sidebands are amplified and higher harmonics appear because of the instability process.

Spatially resolved output spectrum of the self-trapped beam. Left: spectrum in logarithmic scale. Right: Density plot in linear scale of the area marked by the white square on the left. As a lateral beam displacement is associated with the presence of an antisymmetric mode (see Fig.1), the dip in the center of the spectral sidebands is the signature of the soliton beam undulations, i.e., of the snake instability.

Wavelength dependent output profiles. Spatial profiles of the sideband at 1512 nm (red curve) and of the main peak at 1530 nm (dark curve). The dip is exactly located at the beam center as expected from theory (blue curve [16]). The discrepancy between theory and experiment is due to the growth of both antisymmetric and symmetric unstable modes.